Transcription of บทที่ 1 การวิเคราะห์สัญญาณ
1 1 (Fourier series) (periodic signal) (nonperiodic signal) (Fourier transform) (time domain) (frequency components) (frequency domain) ()gt (period) oT ( )() ;0oog tg t TT ( ) ()gt 01( )cos(2)sin(2)nonong taanf t bnf t ( ) na nb (cosine) (sine) of (fundamental frequency) ()gt 1/oofT na nb 2( ) cos2( ) sin.
2 22 /ooooootTnototTnooootoag tn tdtTbg tn tdtfTT ( ) 2 0a (mean value) ()gt (dc component) ()gt 0a 01()oootTtoag t dtT ( ) ( ) 01( )cos() ;2nonoong tCCn tf ( ) 00221tannnnnnnCaCa bba ( ) ( ) (exponential) cos2sin2oooojn tjn tojn tjn toeenteentj ( ) ( ).
3 2ojn tnoong tG ef ( ) nG (complex coefficient) 1()ooootTjn tntoGg t edtT ( ) nG 3 ||njnnGG e ( ) (amplitude spectrum) (phase spectrum)
4 (line spectra) (discrete spectra) ()kt k(t) A To t ()kt ( ) ( ).
5 2ojn tnoonk tK ef ( ) /2/21sinsin2ojn tnoooKAedtTAnAnnnT ( ) 4 nK oT oT ()kt (a) /5oT (b) /2oT (c) 0 A 1A nK sinonoonTAKTnT 0 A 1A 0sin11limonooonTKTTnT ( ) ()kt ( ) 1( )()ojn tonnok tt nTeT ( ) (nonperiodic signal) ()pgt (b) oT oT (infinity) ()pgt ()gt (a) 5 lim( )( )opTg tg t ( )
6 012 010 09 07 05 03 0 011 02 0n 02 0n 012 010 09 07 05 03 0 011 nKnK0009 07 05 03 0 0 03 05 07 09 0 03 03 0 (c)(b)(a) ()kt [Lathi, 1989] ()gtt()pgt0T0Tt0(a)(b) [Lathi, 1989] 6 ()pgt ()gt oT ()pgt ( );2ojn tpnoong tG ef ( ) /2/21()oooTjn tnpToGg t edtT ( ) 2/ooT oT 0o ( ) (infinite) oT 0o 2 /2 /ooT ( ) oT /2/2()
7 OoTjn to npTT Gg t edt ( ) onTG ()Gn ()onT G G n ( ) ( ) ( ) ()()()2jn tpnojn tnGng teTGne ( ) ()pgt 0,, 2, 3, ()pgt ( 0 ) 7 ()Gn ()( )G nG 0 oT ( )( )pg tg t 01( )lim( )lim()2ojntpTng tg tG ne ( ) 1( )( )2jtg tGe d ( ) ( ) ( ) /2/2()lim( )()oooTjn tpTTjn tG ng t edtg t edt ( )( )jtGg t e dt ( ) ()G ( ) ( ) ()gt ()gt ()G ()gt ( ) ( )
8 (Fourier transform pair) ()G [()gt] ()gt ()G ()gt 1 [()G ] ()gt ( )( )g tG ( ) 8 ()gt ()gt ()G 1. ()gt 2. ()gt (absolutely integrable) | ( ) |g t dt 2 Dirichlet (strictly necessary) ()gt ()G ( ()Gf f) ()gt (continuous spectrum) ()G ()( ) | ( ) |gjGGe ( ) | ( )
9 |G ()gt ()g ()gt ()gt *( )( )GG | () | | ( ) |GG ()( )gg 1. (even function) (vertical axis) 2. (odd function) ()ate u t (a) ( )( )atg te u t 9 1()0tan ( )22( )( )101atj ta j tjaGe u t e dtedtaajea 221| ( ) |Ga 1( )tanga (b) | ( ) |G ()g ()gt 0t1()gt()ate u t (a)()G 1a2 ()g 2 0(b) ()
10 Ate u t 10 1. a ()ate u t a ()ate u t ( ?) 2. | ( ) |G ()g
